He was a puzzler and pseudo-science debunker—good stuff already, I’d say—when Scientific American gave him a column in 1956. Over the next quarter century, “Mathematical Games” turned Martin Gardner into a household name to mathematics buffs around the world.
His always thought-provoking pieces brought letters by the hundreds to the magazine. Today, when you push a virtual button to leave a comment, put that number in perspective: you had to write your letter, fold it into an envelope, address and stamp it, toss it in a mailbox.
That Gardner got hundreds of those kind of letters might be the finest measure of the man’s passion. In a real sense, I grew up on his topological oddities, his play with numbers, his infinite curiosity about the world of mathematics. The letters showed how well he transmitted that curiosity to readers like me.
Lessons for us more fly-by-night purveyors of mathematical thoughts, there.
Some of Gardner’s most popular columns were his regular collections of puzzles. Solving one always gave me a thrill, if an admittedly rarely-felt one. It’s his birthday on 21 October—he would have been 98—so let me doff my hat to the man with a small grab-bag, for you, of some of my favourite puzzles.
1) A priest lives at the bottom of a hill. At the top is a temple. Once a year, he makes a pilgrimage up there. He sets off at dawn, stops to rest and eat and admire the view, and reaches the temple by sunset. Three days of prayer follow. At dawn on the fourth day, he sets off again, stops to rest and so on, and strolls into his home a little before sunset, because it’s faster coming down than going up.
Question: Is there a point on the hill at which this pious soul was at the same time on both days? Don’t give me the point, nor the time; just a “Yes”, “No” or “Maybe”, with foolproof reasoning.
2) At 9am, the Deccan Rani leaves Mumbai for Pune, chugging at a steady 60kmph. Also at 9am, the Dunkin’ Raja leaves Pune for Mumbai, doing 40kmph. Assume Mumbai and Pune are 200km apart. Also at 9am, Pappu, a speedy fly, leaves Mumbai, zipping along the track towards Pune at 200kmph (I did say speedy). When he meets the Raja, Pappu turns and flies back until he meets the Rani, turns and flies back towards the Raja…back and forth like this, until he is crushed between the trains.
Question: Never mind the trains, how far has Pappu flown?
3) A room has a number of bulging sacks. You’re told they all contain gold coins, each of which weigh 10g. Except for one sack. It contains counterfeits, each of which weighs either 9g or 11g.
Your job: in exactly one weighing on a digital scale, find the sack with the fakes. If you want it, there’s a felt pen available.
4) Several boxes of medicine have to be transported on foot from Jaisalmer across the desert to Jodhpur. That’s a blazing hot six-day journey, but travellers can carry food and water for only four days at a time.
Question: If Kanakadurga needs to deliver the drugs in Jodhpur six days from now, what’s the minimum number of fellow travellers who must set out with her from Jaisalmer today? There’s this trivial consideration: nobody can die. (Adapted from the puzzle archives of the popular US radio show “Car Talk”).
5) Mr Humayun Sharma has been busy. He has strung a rope right around the earth along the equator, like a 40,000km long belt. Along comes Mr Deepak Khan. He wants Sharma to raise the rope an even 2m off the surface, all the way around the planet, so he can walk upright under it.
Question: Clearly, Sharma will need to lengthen his rope—but by how much? If you can’t give me the exact figure, give me an idea of its magnitude: is it a huge length of extra rope? A tiny bit? What? Why?
6) You and Vishy Kasparov sit down at a chessboard. Instead of making a move, he pulls out 32 domino pieces, each exactly the size of two adjacent squares on the chessboard. He lays them out so they cover the entire board.
Now Vishy pulls out scissors and carefully cuts away the bottom-left and top-right (i.e., diagonally opposite) squares on the chessboard, leaving just 62 squares. He hands you 31 dominoes. “Cover the board!” he says.
Question: Can you do it? Whatever your answer, would it be different if Vishy had cut away the bottom-left and top-left squares?
(Martin Gardner posed both #5 and #6 to his readers).
Have fun! Send me your answers at the address below; also let me know if these were easy or difficult. Hundreds of messages, rivalling Gardner’s Scientific American hauls, would be nice. So would even a few, actually.
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers will explore the joy of mathematics, with occasional forays into other sciences.
To read Dilip D’Souza’s previous columns, go to www.livemint.com/dilipdsouza